Details

sample436.0ms

Algorithm

intervals

Results

251.0ms	4011×	body	80	nan
44.0ms	165×	body	640	valid
8.0ms	43×	body	320	valid
3.0ms	8×	body	1280	valid
2.0ms	15×	body	160	valid
2.0ms	25×	body	80	valid

simplify28.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	51	19
1	156	19
2	907	19
3	5001	19

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.7b

localize22.0ms

Local error

Found 4 expressions with local error:

2.4b	(- (sqrt (+ t 1.0)) (sqrt t))
3.0b	(- (sqrt (+ y 1.0)) (sqrt y))
3.2b	(- (sqrt (+ x 1.0)) (sqrt x))
3.6b	(- (sqrt (+ z 1.0)) (sqrt z))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
32×	`*-un-lft-identity` `sqrt-prod`
16×	`difference-of-squares`
12×	`distribute-lft-out--` `add-log-exp`
4×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out`

Counts

4 → 76

Calls

4 calls:

8.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
11.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
8.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
8.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

series290.0ms

Counts

4 → 12

Calls

4 calls:

73.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
73.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
68.0ms	(- (sqrt (+ x 1.0)) (sqrt x))
75.0ms	(- (sqrt (+ z 1.0)) (sqrt z))

simplify43.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	472	702
1	1521	635
2	5001	620

prune400.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 1.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
2.4b	(- (sqrt (+ t 1.0)) (sqrt t))
3.0b	(- (sqrt (+ y 1.0)) (sqrt y))
3.2b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

86×	`*-un-lft-identity`
44×	`sqrt-prod`
40×	`add-sqr-sqrt`
30×	`distribute-lft-out`
24×	`times-frac`
16×	`add-cube-cbrt`
12×	`difference-of-squares`
10×	`add-log-exp`
9×	`distribute-lft-out--`
6×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
4×	`pow1` `associate-/l*`
3×	`sub-neg` `flip3--` `diff-log` `flip--`
2×	`flip3-+` `associate-/r/` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 107

Calls

4 calls:

16.0ms	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
8.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
8.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
8.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series355.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
72.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
74.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
66.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify63.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	627	1071
1	2344	979
2	5002	943

prune533.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.6b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
0.1b	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
2.4b	(- (sqrt (+ t 1.0)) (sqrt t))
3.0b	(- (sqrt (+ y 1.0)) (sqrt y))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

118×	`*-un-lft-identity`
52×	`sqrt-prod`
45×	`distribute-lft-out`
43×	`add-sqr-sqrt`
42×	`times-frac`
27×	`add-cube-cbrt`
12×	`associate-/r*`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp` `difference-of-squares`
7×	`associate-/l*`
6×	`distribute-lft-out--`
4×	`pow1` `associate-/r/`
3×	`flip3-+` `flip-+`
2×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-exp` `clear-num` `flip--` `div-inv` `associate-/l/`

Counts

4 → 129

Calls

4 calls:

10.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
13.0ms	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
11.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
8.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

series610.0ms

Counts

4 → 12

Calls

4 calls:

318.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
140.0ms	(/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z)))
74.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
77.0ms	(- (sqrt (+ y 1.0)) (sqrt y))

simplify68.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	721	1296
1	2733	1177
2	5001	1135

prune595.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.6b

localize35.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z))) 3)
2.4b	(- (sqrt (+ t 1.0)) (sqrt t))
3.0b	(- (sqrt (+ y 1.0)) (sqrt y))
8.9b	(cbrt (pow (/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z))) 3))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

224×	`*-un-lft-identity`
96×	`times-frac`
90×	`distribute-lft-out`
80×	`sqrt-prod`
66×	`cbrt-prod` `add-sqr-sqrt`
60×	`unpow-prod-down` `cube-prod`
50×	`add-cube-cbrt`
8×	`associate-/r/` `add-log-exp` `difference-of-squares`
7×	`add-exp-log` `add-cbrt-cube`
6×	`distribute-lft-out--`
5×	`pow1`
4×	`flip3-+` `flip-+` `div-inv`
3×	`pow-unpow`
2×	`cube-div` `cube-mult` `sub-neg` `flip3--` `diff-log` `unpow3` `pow-exp` `flip--` `rem-cube-cbrt` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `cbrt-div` `pow-pow` `pow1/3` `div-exp` `rem-cbrt-cube`

Counts

4 → 194

Calls

4 calls:

15.0ms	(pow (/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z))) 3)
8.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
8.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
17.0ms	(cbrt (pow (/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z))) 3))

series581.0ms

Counts

4 → 12

Calls

4 calls:

303.0ms	(pow (/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z))) 3)
67.0ms	(- (sqrt (+ t 1.0)) (sqrt t))
68.0ms	(- (sqrt (+ y 1.0)) (sqrt y))
142.0ms	(cbrt (pow (/ (+ 1.0 0) (+ (sqrt (+ z 1.0)) (sqrt z))) 3))

simplify93.0ms

Algorithm

egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	809	2380
1	3497	2035
2	5001	1947

prune610.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.6b

regimes512.0ms

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	24
1	51	24
2	51	24

end0.0ms

sample1.7s

Algorithm

intervals

Results

989.0ms	15973×	body	80	nan
173.0ms	685×	body	640	valid
42.0ms	208×	body	320	valid
9.0ms	71×	body	160	valid
8.0ms	25×	body	1280	valid
6.0ms	89×	body	80	valid